Abstract
Modern logistics processes and systems can feature extremely complicated dynamics. Agent Based Modeling is emerging as a powerful modeling tool for design, analysis and control of such logistics systems. However, the complexity of the model itself can be overwhelming and mathematical meta-modeling tools are needed that aggregate information and enable fast and accurate decision making and control system design. Here we present Koopman Mode Analysis (KMA) as such a tool. KMA uncovers exponentially growing, decaying or oscillating collective patterns in dynamical data. We apply the methodology to two problems, both of which exhibit a bifurcation in dynamical behavior, but feature very different dynamics: Medical Treatment Facility (MTF) logistics and ship fueling (SF) logistics. The MTF problem features a transition between efficient operation at low casualty rates and inefficient operation beyond a critical casualty rate, while the SF problem features a transition between short mission life at low initial fuel levels and sustained mission beyond a critical initial fuel level. Both bifurcations are detected by analyzing the spectrum of the associated Koopman operator. Mathematical analysis is provided justifying the use of the Dynamic Mode Decomposition algorithm in punctuated linear decay dynamics that is featured in the SF problem.
Highlights
An agent-based model (ABM) is a computational technique in which behavior of individual agents is encoded by simple rules, and the outcomes are observed at the scale of the system [1]
In the Results section we describe the results of the Medical Treatment Facility (MTF) and ship fueling (SF) logistics simulations and the understanding of their dynamics made possible by Koopman Mode Analysis (KMA)
The observable value used as the Koopman Mode Decomposition (KMD) input was the MTF “fullness,” defined as the ratio of the occupancy of each MTF to its capacity
Summary
An agent-based model (ABM) is a computational technique in which behavior of individual agents is encoded by simple rules, and the outcomes are observed at the scale of the system [1]. Simple rules of behavior for individuals can lead to complex, system-scale emergent phenomena [2, 3]. ABMs are relevant to modern modeling problems because their essential feature of interacting micro-scale agents leading to macro-scale dynamics resembles many of the decentralized, highly-interacting social [4,5,6,7,8,9] and economic [10, 11] systems of today. Beyond demonstrating the existence of emergent phenomena for their own sake, the prime importance of ABM results is their analysis for the purpose of decision making. Demare et al [13] studied a highly-
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